Decomposing a Planar Graph into Degenerate Graphs
Copyright policy )Decomposing a Planar Graph into Degenerate Graphs
A graph \(G\) is \(k\)-degenerate if every subgraph of \(G\) has a vertex of degree less than \(k\). The author proves that the vertex set of any planar graph can be decomposed into two sets such that one of them induces a 3-degenerate graph and the other induces a 2-degenerate graph. He also proves that the vertex set of any planar graph can be decomposed into two sets each of which induces a subgraph with no cycle of length larger than three.
- Technical University of Denmark Denmark
decomposition, \(k\)-degenerate, Computational Theory and Mathematics, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), planar graph, Discrete Mathematics and Combinatorics, Paths and cycles, Planar graphs; geometric and topological aspects of graph theory, Theoretical Computer Science
decomposition, \(k\)-degenerate, Computational Theory and Mathematics, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), planar graph, Discrete Mathematics and Combinatorics, Paths and cycles, Planar graphs; geometric and topological aspects of graph theory, Theoretical Computer Science
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).30 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!